par.eCAR.Leroux: R wrapper that accesses C code to fit parametric Leroux CAR...

In eCAR: Eigenvalue CAR Models

R wrapper that accesses C code to fit parametric Leroux CAR spatial regression model that accounts for spatial confounding

Description

par.eCAR.Leroux is the main function used to fit the parametric Leroux CAR model specified in the spectral domain.

Usage

par.eCAR.Leroux(y, x, W,
                E=NULL,
                C=NULL,
                model="Gaussian",
                joint_prior_lamx_lamz = FALSE,
                lamx.fix.val = NULL,
                sig2x.fix.val = NULL,
                mb=0,s2b=10,
                mg=0,s2g=10.0,
                alamx=1, blamx=1,
                alamz=1, blamz=1,
                asig=1, bsig=1,
                atau=1, btau=1,
                asigx=1, bsigx=1,
                mb0=0,s2b0=100,
                me=0,s2e=100,
                mx=0,s2x=100,
                tau_cand_sd = 1,
                sig2_cand_sd = 1,
                draws=10000, burn=5000, thin=5,
                verbose=TRUE)

Arguments

y	response vector
x	covariate vector for which casual effect is desired
W	neighborhood matrix comprised of zeros and ones
E	This argument is ignored if model is Gaussian. For other models it takes on the following: Poisson - E is vector that contains expected counts Binomial - E is vector that contains number of trials Negative Binomial - E is vector that contains an offset.
C	design matrix for the covariates that are included as controls
model	Specifies the likelihood or data model. Options are "Gaussian", "Poisson", "Binomial", "Negative Binomial"
joint_prior_lamx_lamz	Logical. If TRUE, then a uniform prior on space such that lamz > lamx. If FALSE, independent beta priors are used.
lamx.fix.val	If a value is supplied then lambda_x is not updated in the MCMC algorithm, but rather treated as the fixed known supplied value
sig2x.fix.val	If a value is supplied then sigma2_x is not updated in the MCMC algorithm, but rather treated as the fixed known supplied value
mb	prior mean for beta. default is 0.
s2b	prior variance for beta. default is 10
mg	prior mean for gamma, where gamma = rho*(sigz/sigx). default is 0.
s2g	prior variance for, gamma), where gamma = rho*(sigz/sigx). default is 10
alamx	prior shape1 parameter for lam.x, default is 1. Only used if joint_prior_lamx_lamz = FALSE
blamx	prior shape2 parameter for lam.x, default is 1. Only used if joint_prior_lamx_lamz = FALSE
alamz	prior shape1 parameter for lam.z, default is 1. Only used if joint_prior_lamx_lamz = FALSE
blamz	prior shape2 parameter for lam.z, default is 1. Only used if joint_prior_lamx_lamz = FALSE
asig	prior shape parameter for sigma2, default is 1. Only used if model is Gaussian
bsig	prior scale parameter for sigma2, default is 1. Only used if model is Gaussian
atau	prior shape parameter for tau, where tau = sigma2.z*(1-rho^2). default is 1
btau	prior scale parameter for tau, where tau = sigma2.z*(1-rho^2). default is 1
asigx	prior shape parameter for sigma2.x, default is 1
bsigx	prior scale parameter for sigma2.x, default is 1
mb0	prior mean parameter for beta0, default is 0. Only used if model is not Gaussian
s2b0	prior variance parameter for beta0, default is 100. Only used if model is not Gaussian
me	prior mean parameter for eta, default is 0. Only used if C is not NULL
s2e	prior variance parameter for eta, default is 100. Only used if C is not NULL
mx	prior mean parameter for xi, default is 0. Only used for negative binomial model
s2x	prior variance parameter for eta, default is 100. Only used for negative binomial model
tau_cand_sd	standard deviation for candidate density in Metropolis step for tau. Default is 1
sig2_cand_sd	standard deviation for candidate density in Metropolis step for sig2. Default is 1. Only used if model is Gaussian
draws	number of MCMC iterates to be collected. default is 10000
burn	number of MCMC iterates discared as burn-in. default is 5000
thin	number by which the MCMC chain is thinned. default is 5
verbose	If TRUE, then details associated with data being fit are printed to screen along with MCMC iterate counter

Value

The function returns an eCAR object which is a list that contains the following

data_model	Character indicating which model was fit
beta_omega	Matrix that contains respectively, the posterior mean lower and upper quantiles of the (spatial scale)-varying beta at each omega value (for the non Gaussian cases it is the exponentiated beta).
posterior_draws	List containing posterior draws of the following parameters beta: vector containing draws from the posterior distribution of exposure coefficient gamma: vector containing draws from the posterior distribution of gamma=rho*(sigz/sigx) tau: vector containing draws from tau=sigma2.z*(1-rho^2) sig2x: vector containing draws from sig2x lamx: vector containing draws from the posterior distribution of lamx lamz: vector containing draws from the posterior distribution of lamz sigma2: vector containing draws from the posterior distribution of sigma2. Only available if model is Gaussian rho: vector containing draws from the posterior distribution of rho sig2z: vector containing draws from the posterior distribution of sig2z theta: matrix containing draws from the posterior distribution of theta. Only available if model is not Gaussian beta0: vector containing draws from the posterior distribution of beta0. Only available if model is not Gaussian eta: matrix containing draws from the posterior distribution of eta, regression coefficients of additional confouner variables. Only available if C is not NULL nb_r: matrix containing draws from the posterior distribution of nb_r. 0nly available if model is Negative Binomial
DIC	Not available from parametric model yet
regrcoef	Not available from parametric model yet

References

Guan, Y; Page, G.L.; Reich, B.J.; Ventrucci, M.; Yang, S; "A spectral adjustment for spatial confounding" <arXiv:2012.11767>

Examples

# Our R-package
library(eCAR)

data(lipcancer)


W <- lipcancer$neighborhood.Matrix
M <- diag(apply(W,1,sum))
R <- M-W
e.dec <- eigen(R)
e.val <- e.dec$values
D.eigval = diag(e.val)


Y <- lipcancer$data$observed
X <- lipcancer$data$pcaff
E <- lipcancer$data$expected

set.seed(101)
fit1 <- par.eCAR.Leroux(y=Y, x=X, W=W, E=E, C=NULL, model="Poisson",
                         draws=10000, burn=5000, thin=1, verbose=FALSE,
                         joint_prior_lamx_lamz=FALSE)


plot(fit1)

eCAR documentation built on April 5, 2023, 5:09 p.m.